"It sucks right now, but I'm playing next week". He birdied the 17th and 18th holes in regulation to get into the playoff with Ryan Moore and Brandt Snedeker, then birdied the 18th hole two more times to start the playoff before the players movee to the 10th hole.
Snedeker appeared to have things on cruise control at the Safeway Open, torching the North Course at Silverado Resort & Spa en route to a three-shot lead entering the final round.
"I have to find a way to win today", Snedeker tweeted. "Played a really good front nine in tough conditions and made the turn on the back nine and actually drove the ball really well".
Starting his 19th full season on the tour, Baddeley, 37, could not quite add to his four victories there but added $241,280 ($A342,000) to his $US20,543,617 in career earnings while some younger countrymen also impressed.
"I'm kind of at a loss for words", he said afterwards.
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"I think he's probably crying to be honest", said Tway of his father, who had been watching on television.
Tway, the son of 1986 PGA Championship victor Bob, was in a three-way race for the title after going around in 71 in the final day and finishing on 14-under alongside compatriots Ryan Moore and Brandt Snedeker. "He's pretty proud of me".
"It's been a long road but this is why you work hard".
The trio finished regulation at 14-under 274, one stroke ahead of five others.
Moore matched Tway's birdies at the first and second playoff holes, before succumbing at the third - the par-four 10th. Troy Merritt carded a 68, Sam Ryder and Australian Aaron Baddeley fired 69s and Web.com Tour graduate Im Sung-jae of South Korea posted a 71 to complete the group at 13-under.